Are there any privacy search tools that avoid ad profiling for sensitive query lookup?

Yes. If your goal is to look up sensitive topics without feeding ad profiles, the main thing is to use a search engine that does not track you across searches or build an advertising profile. Good options include:

Privacy-focused search engines

• DuckDuckGo — does not personalize results using your search history and does not build an ad profile tied to you.
• Startpage — serves Google results, but acts as a privacy proxy so Google doesn’t get your identity/IP directly.
• Brave Search — designed to avoid user-level tracking and profiling.
• Searx / SearxNG — open-source metasearch engine you can self-host or use via public instances; privacy depends on the instance.

Tips for sensitive searches

• Use a private/incognito window.
• Prefer a browser with stronger privacy defaults, like Brave, Firefox with tracking protection, or LibreWolf.
• Disable or limit third-party cookies.
• Avoid being logged into Google, Bing, or social accounts while searching.
• Consider using a VPN or Tor if you want to reduce network-level linking.

Important caveat

Even privacy search engines may still:

• see your search terms,
• receive your IP address unless you use Tor/VPN,
• and sometimes show ads that are contextual rather than profile-based.

If you want, I can also give you a short comparison table of DuckDuckGo vs Startpage vs Brave Search for sensitive queries.